3156
Journal of the American Chemical Society
lengths are: e~perimental,~' 125-128 6)",1.545 (5) A, not determined; Allinger 1971, 126.9', 1.541 A, 1.552 Allinger 1973, 128.6", 1.546 A, 1.548 A; Schleyer, 126.7', 1.540 A, 1.551 A; MUB-2, 122.6", 1.541 A, 1.552 A. L. S. Barteli and W. F. Bradford, J. Mol. Struct., 37, 113 (1977). G. P. Hellmann, Ph.D. Thesis, Universitlt Freiburg, 1977, p 45. W. Klyne and V. Prelog, Experientia, 16, 521 (1960). 0. Bastlansen, F. N. Frltsch, and K. Hedberg, Acta Crysta//ogr., 17, 538 (1964). J. F. Liebman and A. Greenberg, Chem. Rev., 76, 311 (1976): cf. pp 329-330.
A;
(31) (32) (33) (34) (35)
/
1OO:lO
/ May 10, 1978
(36) We thank Dr. Paul Blckart for this suggestion. (37) E. Ruch, W.W l b a r t h , and 8. Richter, W .Chim. Acta, 19,286 (1970): W. Hasselbarth and E. Ruch, ibid., 29, 259 (1973). (38) J. G. Nourse, J. Am. Chem. SOC.,99, 2063 (1977). (39) For notation, cf. J. G. Nourse and K. Mislow, J. Am. Chem. SOC.,97,4571 (1975). (40) The conjugacy classes of S, and the cycle structure of the wreath products necessary for L can be found in D. E. Littlewood, "The Theory of Group Characters", Clarendon Press, Oxford, 1940, pp 265-284. (41) Note that (34)(56) yields si+ZBFBz. A representative of that double coset could equally well have been chosen to give re-FzBFBZ (e.g., (23)(45)).
Strained Small Ring Compounds. Structure of a Substituted Semibullvalene, 1-Cyanotricyclo[ 3.3.0.0238]octa-3,6-diene. Geometric Evidence for Homoaromaticity in the Molecular Ground State Gary G. Christoph" and Mark A. Beno Contribution from the Evans Chemical Laboratories, Chemistry Department, Ohio State University, Columbus, Ohio 43210. Received September 7 , 1977
Abstract: The structure of 1-cyanosemibullvalene (1 -cyanotricyclo[3.3.0.02~E]octa-3,6-diene, C9H7N) has been determined by high-resolution x-ray crystallographic methods at -45 " C . The molecule exists wholly in the tautomeric form possessing the cyclopropane ring C( l)-C(2)-C(8). The extraordinarily long C(2)-C(8) bond distance (1 S77 A, corrected for thermal libration) and the shortened distance between the formally nonbonded atoms C(4) and C(6) (2.35 A), together with the lack of indication of severe repulsive strain, are evidence for a small but significant homoaromatic stabilization in the molecule. The interaction between C(4) and C(6) is accordingly deduced to be attractive, however with an estimated bond order of no more than 0.10 for the p-p u overlap between these two atoms. l-Cyanosemibullvalene forms colorless, prismatic crystals having the orthorhombic space group P212121. The cell constants are a = 6.693 (2), b = 8.301 (3), c = 12.393 (4) (MoKa, T = -45 "C). There are four molecules per cell, each possessing nearly perfect noncrystallographic mirror symmetry. The final R factors for 1192 reflections are R = 0.056 and R, = 0.066.
Introduction Small ring hydrocarbons are particularly interesting compounds because their high energy content relative to the acyclic isomers often endows them with unusual reactivity patterns. Occasionally, such compounds are remarkably unreactive and stable, usually because rearrangement to a less highly strained system must go via an even more highly strained state or because direct rearrangements are forbidden by symmetry rules.' In either case, the reactivity, or lack of it, is strongly determined by the molecular structure; one is immediately led to the general question of how the "strain" inherent in these molecules is expressed; is it accumulated in one or two bonds or is it distributed throughout the molecule? Further, what is the effect on the strained system (and on its reactivity) of various substituent groups? Sufficient numbers of small monocyclic hydrocarbons have been examined that the direct substituent effects on such compounds, if not clearly predictable, are at very least regular and understandable in terms of steric, electronic, and inductive effects. More unusual situations arise in which a small ring system is either further strained or constrained by fusion with other small rings. Abnormal molecular geometries can be generated in this fashion and the reactivity patterns of these and similar compounds have attracted much synthetic and kinetic attention.* In this and subsequent papers we will examine the structures of highly strained polycyclic hydrocarbons with the aim of finding the structural bases for their reactivities. The bridged homotropilidenes bullvalene (I), dihydrobullvalene (II), barbaralane (III), and semibullvalene (IV) are
I
Pa
m
II
Yb
Ip
Yc
fluxional in the sense that internal Cope rearrangements (e.g., Va Vc) are fairly facile, with calculated energies of activation on the order of 3-1 5 kcal/moL3 These molecules are of considerable current interest because the transition states of such rearrangements are in theory homoaromatic, and the possibility exists of preferentially stabilizing the transition state relative to the ground state in molecules of this type with appropriate substituents4 and of thus isolating the first derivatives of bishomobenzene (VI).
-1
I
k;
m Cheng, Anet, Mioduski, and MeinwaldS have recently measured the free energy of activation for the degenerate Cope
0002-7863/78/1500-3156$01.00/0 0 1978 American Chemical Society
Christoph, Beno
/ I -Cyanotricyclo[3.3.0.02~8]octa-3,6-diene
3157
Table I. Crystal Data 1-Cyanotricyclo[3.3.0.02~x]octa-3,6-diene, C9H7N
..
Mol wt 129.16 M p 50.5-51 'C Space group: orthorhombic, P212121(no. 19) Cell constants: a = 6.693 (2) 8, b = 8.301 (3) 8, c = 12.393 (4) 8, V = 688.6 (4) A3
Density (calculated, Z = 4) 1.246 g cm-3 Radiation: Mo Ka X = 0.710 69 8, Absorption coeff p(Mo K a ) = 0.803 cm-l Transmission factors: max 0.992, min 0.967
rearrangement of semibullvalene (IV). The value, 5 . 5 f 0.1 kcal/mol, although larger than that calculated by Dewar and Schoeller3using the M I N D 0 / 2 method, is the lowest known barrier for any compound capable of undergoing the Cope rearrangement. Hoffmann and S t ~ h r e predicted r~~ strong equilibrium preferences for semibullvalenes unsymmetrically substituted a t the 1 or 5 position and further raised the possibility of destabilizing the ground state relative to the transition state by selective symmetrical substitution. Appropriate synthetic methods for introducing such substituents into the semibullvalene nucleus have only recently become available6 and we here describe the structural analysis of l-cyanosemibullvalene, a preliminary report of which has appeared elsewhere.7
Experimental Section Colorless, irregular, prismatic crystals of the title compound were sealed into thin-wall glass capillaries. Since the compound is subject to slow thermal decomposition at room temperature, all measurements were made on one crystal (0.1 X 0.1 X 0.4 mm) at -45 f 5 ' C , using an automated Syntex diffractometer equipped with a cold gas stream low-temperature device. Cell constants were determined by leastsquares fit of the setting angles of eight carefully centered medium intensity reflections for which 19' 5 20 I27'. The space group was determined to be P212121 by inspection of the systematic absences (hOO, h = 2n 1; OkO, k = 2n 1; 001, I = 2n 1) after thecompletion of the data collection. Reciprocal space was surveyed at half-integral values of the Miller indexes to ensure that the unit cell size was correct. Cell constants and other crystal data are given in Table I. Intensity data were collected using the W-20 scan technique, with a scan width which varied linearly with sin 0 to accommodate a1-a2 splitting. The scan rate was adjusted between the limits of 1.0 and 12.O0/min on the basis of a quick premeasurement of peak intensity. All intensities in one octant were measured for which 0' I 20 5 60'. The intensities of four reflections, 042, 117, 141, and 3 10, were remeasured periodically to monitor crystal condition and alignment, and plots of these intensities as a function of x-ray exposure time revealed no observable crystal decomposition. No absorption corrections were necessary. The intensities were reduced to F2's and E's in the usual way, with the estimates of the standard errors in the scattering factor amplitudes made using the formula
+
+
+
where r is the scan rate, Lp is the Lorentz-polarization factor for the monochromatized beam case,8 S, B 1, and B2 are the scan and background counts, G is the ratio of scan time to total background counting time, I is the net intensity (= {S - G(BI B2))), a n d p is a factor, chosen as 0.02, included in a term presumed to represent that component of the total error expected to be proportional to the diffracted i n t e n ~ i t yA. ~total of 1290 reflections were measured. After deleting systematic absences and averaging of multiply measured reflections, 1192 independent reflections remained, of which 825 were greater
+
i
I
t -'
t
-I
Figure 1. Normal probability plot: (Fo2 - F,*)/u(Fo2) vs. calculated normal deviates. The linearity indicates that the model structure accounts well for the observed data, leaving only residual normally distributed error. The slope suggests that on the average the a(Fo2)were underestimated by about 40%. than 3u above background. The R factors for multiply measured reflections (principally the check reflections) were R I = 0.010 and R2 = 0.050.10The distribution of the intensity statistics and a Howells, Phillips, and Rogers plotll verified the acentric space group. The phase problem was solved by direct methods, using the program M U L T A N . ~All ~ nonhydrogen atoms were located on the E map with the highest figure of merit. After several cycles of least-squares refinement of the atomic coordinates and isotropic temperature factors, the hydrogen atoms were readily apparent on a difference map and their coordinates and isotropic thermal parameters were then also refined. Additional refinement using anisotropic thermal parameters for the nonhydrogen atoms and including a secondary extinction parameter') resulted at convergence in final R of 0.056 and R , of 0.066 for 1192 reflections. The final "goodness of fit" was 1 .42.14 The final data-parameter ratio was 9.92. A normal probability plot" of the ) the expected normal deviates for quantities (Fo2 F C 2 ) / u ( F o 2vs. 1192 points (Figure 1) shows that the cr(FO2)were on the average underestimated by about 40%, but that the distribution of error was normal. The linearity of the plot is excellent, and indicates that all systematic trends in the data are satisfactorily accounted for by the derived structural model. Table I1 lists the final values of the parameters varied in the least-squares refinement. Tables of the observed and calculated structure factor amplitudes and cr(Fo2) comprise Table I of the supplementary material.I8 The final difference Fourier map showed no peaks greater than $0.37 or less than -0.32 e Almost all of the remaining features were located in the vicinity of the bonding regions between the atoms. The general noise level of the map was about f0.10 e 8,-3. On completion of the structure solution the program TLSI9 was used to analyze the anisotropic thermal parameters and to obtain bond distances and angles corrected for rigid body librational motion. The program, which was modified to include mass weighting of the atoms,2O gave essentially isotropic molecular translational root mean square amplitudes of 0.16 A and root mean square librational amplitudes of 5.4, 2.9, and 2.2'. The largest amplitude librational motion is about a molecular axis almost exactly parallel to the normal to the plane of atoms C(3)-C(4)-C(7)-C(6). The excellent agreement between the individual atomic thermal parameters and those predicted by the librational model (root mean square error, {ZAu*,/(m - S ) J I / ~
-
3158
Journal of the American Chemical Society
/
1OO:lO
/ May 10, 1978
Table 11. Final Values of Least-Sauares Parameters Atom
X
Y
Z
C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) N H(1) H(2) H(3) H(4) H(5) H(6) H(7)
0.7197 (3) 0.5899 (3) 0.7246 (4) 0.9058 (4) 0.9127 (3) 0.8582 (3) 0.6628 (3) 0.5590 (3) 0.7224 (3) 0.7269 (3) 0.484 (3) 0.677 (3) 1.014 (3) 1.032 (3) 0.950 (3) 0.595 (3) 0.444 ( 3 )
0.4258 (2) 0.5670 (2) 0.7071 (2) 0.6710 (2) 0.5006 (2) 0.5296 (2) 0.5202 (3) 0.4709 (2) 0.2768 (2) 0.1579 (2) 0.554 (2) 0.808 (3) 0.741 (2) 0.442 (2) 0.571 (2) 0.540 (2) 0.410 (2)
0.1278 (1) 0.0993 (2) 0.0953 (2) 0.1290 (2) 0.1739 ( I ) 0.2911 (2) 0.3060 (2) 0.2071 (2) 0.0685 (1) 0.0220 (1) 0.047 (2) 0.074 (2) 0.141 (2) 0.157 (1) 0.342 ( I ) 0.374 (1) 0.208 (1)
PI1
[BI2
115 (4) [2.0] 171 (5) [2.6] 282 (7) [3.1] 231 (6) [3.1] 110 (4) [2.3] 193 (5) [2.7] 203 (5) [2.7] 114 (4) [2.5] 96 (4) [2.1] 150 (4) [2.8] r2.8 (411 [3.2 (5)1 [4.0 (6)1 [2.2 ( 4 ~ l2.1 (411 r2.8 (411 ~ 2 . 2(4)1
+
022
P33
PI2
PI3
023
71 (2) 86 (3) 71 (3) 92 (3) 90 (3) 86 (3) 93 (3) 87 (3) 86 (2) 89 (2)
31 (1) 40 (1) 37 ( I ) 41 (1) 41 (1) 36 (1) 32 (1) 48 (1) 34 (1) 52 (1)
-24 (6) 43 (7) 7 (8) -97 (8) -20 (7) 17 (7) 29 (7) 4 (6) -1 (6) 11 (7)
-4 (4) -38 (5) -2 (6) 33 (6) 9 (4) -45(5) 24 (4) 32 (4) -14 (4) -16(4)
-6 (3) -9(3) 7 (3) -18 (4) -36(3) -l8(4) -8 (4) -9(4) 4 (3) -29 (3)
+ +
a The form of the anisotropic thermal parameter is exp[-2r(h2P1 I k2P22 . . . klP23].The B values given in brackets for the anisotropic atoms are the isotropic equivalent. The values in parentheses are in this and subsequent tables the estimated standard deviation in the least significant digit.
unrealistic results, which we attributed to the inadequate and poorquality data, and we consequently were forced to terminate our analysis.
Description of the Structure The molecular architecture is illustrated in Figure 2. Interatomic distances and angles, uncorrected and corrected for thermal libration effects, comprise Table 111. The molecule possesses nearly perfect mirror symmetry, with the symmetry plane lying in the plane of C(1), C(5), and C(9) and bisecting the cyclopropane ring. The molecule is wholly in the tautomeric ground state VIIa; C(3)-C(4) and C(6)-C(7) are well-locala c6
,,101.4'
\
P
b Figure 2. Thermal ellipsoid (ORTEP) diagrams showing the average values for pertinent chemically equivalent bond distances and angles, and the numbering scheme for the molecule. = 0.0016 A2) indicates that the thermal motions of the atoms are predominantly of librational origin and well accounted for by the model.I8 In any case, in view of the reduced data collection temperature, the resulting bond length corrections are reassuringly small. Because of the interest in the low barrier for the Cope rearrangement, we were curious to see the effect of raising the temperature on the thermal parameters, particularly of C(2) and C(8). A second data set was therefore collected at 21 OC on the same crystal. Because of high thermal motion, thermal decomposition, or crystal decay (at completion the crystal had become nearly opaque and pale yellow in color) the data were neither extensive nor of high quality, with only 248 of the 432 reflections having 28 5 40.0' being more than 3a above background, for comparable counting times. Refinement using as starting coordinates the results of the -45 O C study gave physically
ized double bonds and C(4) and C(6) are, at 2.35 A apart, apparently (vide infra) precluded from significant bonding interaction. The cyclopropane bond lengths are inequivalent, with the C-C bonds proximal to the nitrile of normal length while the distal bond, a t 1.577 A, is substantially longer than even a normal sp3-sp3 carbon-carbon bond. The cyclopentene rings are seriously puckered, the approximately planar C(Z)-C(3)-C(4)-C(S) linkage being folded outward from the C(2)-C(I)-C(5) plane by 19.9'. The angle between the analogous planes on the other side of the molecule is 18.6'. Least-squares plane calculationsi8 show C( 1) displaced from the planes of the other four atoms in each ring by about 0.3 A. C(4) and C(6) similarly lie to the outside of their respective rings, but by only 0.05-0.06 A, as is reflected by the small torsion angles about the two double bonds of 6.7 and 4.9'. With the exception of the bridgehead bond C( l)-C(5), and C-C bond distances in the cyclopentene rings are remarkably close to the values expected for typical bonds of appropriate hybridization (Table IV). The C=N bond is of normal length. Three of the four shortest intermolecular contacts involve the cyano nitrogen atom and hydrogen atoms of C(2), C(5), and C(7) of neighboring molecules, with respective N. .H contact distances of 2.61, 2.70, and 2.70 A. The geometry of the contacts and the expected low acidity of the hydrogen atoms preclude these being interpreted as even very weak hydrogen bonds. One other contact, also essentially van der Waals
Christoph, Beno
/ 1-Cyanotricyclo [3.3.0.02~8]octa-3,6-diene
Table 111. Interatomic Distances
(A) and Angles (deg)
Uncorrected
Correctedu
1.501 (3) 1.504 (3) 1.543 (3) 1.438 (2) 1.569 (3) 1.472 (3) 1.317 (4) 1.521 (3) 1.517 (3) 1.323 (3) 1.467 (3) 1.143 (2) 3.065 (3) 2.349 (3) 0.97 (2) 0.93 (2) 0.94 (2) 0.96 (2) 0.94 (2) 0.97 (2) 0.92 (2)
1.507 1.510 1.549 1.441 1.577 1.478 1.323 1.526 1.523 1.329 1.472 1.145 3.079 2.359 0.97 0.94 0.94 0.97 0.94 0.97 0.92
118 (1) 114(1) 120 ( I ) 115 (1) 121 (1) 123 ( I ) 121 ( I ) 123 (1) . ,
C(l)-C(8)-H(7) C(2)-C(8)-H(7) C(l)-C(2)-H(l) C(8)-C(2)-H(I) C(3)-C(2)-H( 1) C(7)-C(8)-H(7) C( 2)-C( 3)-H( 2) C(8)-C(7)-H(6)
3159
Uncorrected
Correctedu
C(2)-C( 1)-C(8) C( I)-C(2)-C(8) C( I)-C(8)-C(2) C( I)-C(2)-C(3) C( I)-C(8)-C(7) C(2)-C( 1)-c(5) C(8)-C( 1)-C(5) C(2)-C( 1)-c(9) C(8)-C( I)-C(9) C(5)-C( 1)-C(9) C (2) -c(3) -c(4) C(8)-C(7)-C(6) C( I)-C(5)-C(4) C( 1)-C(5)-C(6) C(4)-C(5)-C(6) C(3)-C(4)-C(5) C(7)-C(6)-C(5) C(3)-C(2)-C(8) C(7)-C(8)-C(2)
63.0 (1) 58.6 ( I ) 58.4 ( I ) 105.7 (2) 106.1 (2) 104.9 (2) 104.8 (1) 123.9 (2) 123.8 (2) 121.7 (2) 11 1.9 (2) 111.6(2) 102.3 (2) 102.6 (2) 101.2 (2) 110.8 (2) 11 1.2 (2) 120.7 (2) 120.5 (2)
63.0 58.6 58.4 105.6 106.0 105.0 105.0 123.9 123.8 121.6 112.0 1 11.7 102.2 102.4 101.4 110.9 111.2 120.8 120.5
N-C(9)-C( 1) C(3)-C(4)-C(6) C(7)-C(6)-C(4) C(5)-C(4)-C(6) C(5)-C(6)-C(4) C(4)-C( 3)-H(2) C(6)-C(7)-H(6) C( 3) -C(4) -H (3) C( 7)-C( 6) -H (5) C(5)-C(4)-H(3) C(5)-C(6)-H(5) C( I)-C(5)-H(4) C(4)-C(5)-H(4) c(6j-cis j - ~ ( 4 j
179.0 (2) 105.1 (2) 106.4 (2) 39.3 (1) 39.4 ( 1 ) 127 ( I ) 125 (1) 128 ( 1 ) 125 (1) 120 ( I ) 123 (1) 114(1) 1 I5 ( I ) 120iij
179.0 105.0 106.4 39.2 39.4
Corrected for thermal librational motion; see text.
Table IV. Bond Tvues in 1-Cvanosemibullvalene Typical length,u Bond
A
Atoms
Length, A
C(4)-C(5) C(6)-C(5) C(2)-C(3) C(7)-C(8) C( l)-C(9) C(3)-C(4) C(6)-C(7) C(l)-C(2) C(l)-C(8)
1.526 1.523 1.478 1.472 1.441 1.323 1.329 1.507 1.510
c-c
(spZ-sp3)
1.52
c-c
(sp2-sp2)
1.48
C=N (sp2-sp)
c=c (sp2-sp2)
1.44 1.33
C-C
1.51
cyclopropane (SP5-SP5)
roughly perpendicular to the cyclopentene rings, but found none.
a L. E. Sutton, “Interatomic Distances”, Chem. Soc., Spec. Publ., No. 11 (1958); No. 18 ( 1 965).
in nature, between C(6) and H(3) of another molecule, is 2.68
A. Interatomic contacts less than 3.5 %,are given in the supplementary tables;18 nearly all are hydrogen-hydrogen contacts at normal van der Waals distances. The slight nonlinearity of the nitrile group and the small deviations from molecular C, symmetry, all of normal magnitude, we ascribe to asymmetric packing effects. The atomic thermal vibration amplitudes ranged from 0.14 to 0.25 A, with the larger amplitudes primarily associated with C(4), C(6), and N( 1). Rigid librational motion accounted nearly completely for the observed amplitudes. W e in particular examined the residual amplitudes (observed minus librational) of C(2), C(4), C(6), and C(8) to see if there was any “extra” motion suggestive of a low-energy breathing vibration
Discussion Both the very long C(2)-C(8) distance and the apparent normality of the bond distances in the cyclopentene rings are surprising results: C ( l ) is the point of attachment of the strongly a-accepting cyano group, which is expected by conjugation with the cyclopropane ring to alter its equilateral geometry, but not in the observed direction. If the low-lying unoccupied (a*) orbitals of such a substituent are properly aligned to interact with the antisymmetric component of the highest occupied degenerate Walsh2’ orbital pair in the cyclopropane, the net effect is a delocalization of electron density out of the cyclopropane molecular orbital and into the vicinal a system, Figure 3. Because that cyclopropane molecular orbital is primarily bonding for C( 1)-C(2) and C( 1)-C(8), but antibonding for C(2)-C(8), the loss of electron population from this orbital should result in an increase in the C( 1)-C(2) and C(l)-C(8) bond distances (a net decrease in bond strength) and a simultaneous decrease in the C(2)-C(8) bond distance (an increase in bond strength).22We should further expect to observe some weakening of the C z N bond, as its empty, low-lying antibonding orbital becomes populated. Such conjugative interactions of cyclopropanes with x substituents are amply supported by spectroscopic and chemical data23 and structural studies.24 The structure of 2,5-dimethyl-7,7-di~yanonorcaradiene~~~ (Figure 4) is most germane to our situation: the cyclopro ane bonds proximal to the dicyano substituents are ca. 0.05 longer, and the distal bond is ca. 0.01 %, shorter than in c y ~ l o p r o p a n ein, ~agreement ~
8:
3160
Journal of the American Chemical Society 9
1.600
/ May 10, 1978
1OO:lO a
a
Figure 3. Interaction of cyclopropane Walsh orbital with low-lying cyanide ir* orbital (ref 22).
Figure 5. Structure of semibullvalene as determined by electron diffraction (ref 26). The molecule is assumed to possess mirror symmetry, and C(2)-C(3) and C(4)-C(5) are assumed to be equivalent.
ticular interest here that the puckering of the cyclopentene rings is substantially less than the 29.0’ for cyclopentene28 and that, whereas steric interactions between geminal carbon atoms would be expected to increase the C(4)-C(5)-C(6) angles over the tetrahedral value, they are in both molecules much less than 109.5’. Cycloheptatriene (VIII) in the gas phase has 113’ for
Figure 4. Effect of dicyano substitution on cyclopropane geometry; the vicinal bonds are lengthened while the distal bond is shortened in 1 , l dicyano-3,5-dimethylnorcaradiene (ref 24c).
with the above predictions. In 1-cyanosemibullvalene, however, not only d o we find the proximal cyclopropane bonds, which should be most affected, to be of normal length, but the distal bond is abnormally long. The unusual geometry of the cyclopropane ring could be interpreted as arising from steric repulsion between C(4) and C(6) forcing the cyclopentene rings apart and stretching C(2)-C(8), or, conversely, it could arise from a significant homoaromatic contribution to the molecular ground state, wherein the C(4). C ( 6 ) contact is attractive rather than repulsive, and the C(2)-C(8) bond is lengthened, not by steric forces, but simply by increased antibonding character in compensation for the nascent bond formation between C(4) and C(6). By comparison with related structures, careful analysis will demonstrate that the observed geometry is consistent only with the C(4)- C ( 6 ) contact being attractive, rat her than repulsive. Using gas-phase electron diffraction methods, Wang and Bauer26 determined the structure for the parent hydrocarbon semibullvalene, Figure 5 . One is immediately tempted on the basis of their results to explain the “long” 1.577 8,C(2)-C(8) distance of 1-cyanosemibullvalene as simply the consequence of induced shortening (a 1a’ 1,l -dicyanonorcaradiene) of the cyclopropane bond opposite the cyano substituent. This agrees well with Hoffman’s prediction,22 but leaves the origin of the long C(2)-C(8) distance unexplained. The limited accuracy of Wang and Bauer’s determination2’ makes us reluctant to use this argument; the two structures cannot be reliably compared in such fine detail. In spite of differences between some of the bonding parameters, however, the general conformations of the two molecules are in substantial agreement: In both cases the cyclopentene rings are puckered, with C(4) and C(6) folded outward by about 18’; the C(2)-C(8) distances in both are extraordinarily large; and the two double bonds in each case appear to be well localized and essentially planar. It is of par-
-
2
3
IX VI11 the value of analogous angle, and the C(4). C ( 6 ) distance is 2.51 A.29 Slightly different results were found in IX, the structure of the p-bromophenacyl ester of 7,7-dimethyl-3carboxylic acid derivative of cycloheptatriene: 106’ and 2.42 A.30The completely unstressed nonbonded distance expected for two carbon atoms each 1.525 A from a common tetrahedral carbon center would be 2.490 A. Another expected consequence of steric repulsion between C(4) and C(6) would be larger than normal dihedral angles between the cyclopentene and the cyclopropane rings. In order to evaluate this more fully we compare these angles (calculated as the angle between the cyclopropane plane and the plane defined by the common and two adjacent carbon atoms of each of the cyclopentene rings) in Table V with those for similarly constituted planes in simple bicyclic systems having a cyclopropane ring fused to a five-, a six-, or a seven-membered ring, but not subject to the constraints imposed by further ring fusions. The dihedral angles for I -cyanosemibullvalene are, although somewhat greater than the average, still well within the range of values for the unconstrained bicyclic systems, again indicative of the absence of substantial repulsive strain between the cyclopentene rings. Very short intramolecular nonbonded C. .C contacts between juxtaposed carbon atoms have been observed in a few systems, most notably in certain 1,6 methano-bridged [ 101annulenes (e.g., 2.27 A in X31) and cyclophanes (2.69 A in
-
X
XI
XI32).The former contain the cycloheptatriene structural unit and are similarly capable of a Cope rearrangement to a norcaradiene type structure. The ring of completely alternating double bonds in the annulene bestows considerable aromatic character on the molecule, thus providing an extra driving force
Christoph, Beno
/ 1 -Cyanotricyclo[3.3.0.02~8]octa-3,6-diene
3161
Table V. Dihedral and Bond Angles in Some Bicyclic Systems 1
Compd
Ring size
Dihedral angle
L123 (L123')
Africanol
7
108.0
121.0
cis-Bicyclo[5.1 .O]-oct-4-exo-y1 p-bromobenzoatesulfonate
1 1 1.0 125.4 112.3
7-Dimethoxyphosphoryl-7-phenylnorcaradiene 2,5-Dichloro-7-dimethoxyphosphoryl-7-phenylnorcaradiene exo-7-Chloro-7-phenyI-2,5-dioxabicyclo[4.1 .O] heptane 2,5-Dimethyl-7,7-dicyanonorcaradiene Axivalin hydrate
7 7 6 6 6 6 6 6
Benzocyclopropapyran
6
110.2
6-0xo-3a,5-cycloandrostan- 17-ylp-bromobenzoate
5
111.5
121.6 119.0 119.9 119.8 119.6 121.1 118.4 118.4 (116.4) 120.7 (123.4) 115
syn-8,8-Dichloro-4-phenyl-3,5-dioxabicyclo[5.1.O]octane endo-7-Chloro-7-phenyl-2-oxabicyclo[4.1 .O] heptane
111.1 1 10.4
111.1 108.1
107.9
L145 (L145') 114.8 (114.7) 121.2 119.5 124.0 120.3 119.0 119.8 117.5 119.7 123.1
6-0xo-3~,5-cycloandrostan17-yl acetate
5
111.5
115.9
6,6-Diphenyl-3,3-diethyl-3-azabicyclo[ 3.1.O] hexane
5
115.0
120.8
120 (117) 118.4 (114.6) 118.7
5 5 5 5
116 117 116.7 116.2
119.4 104.8 104.9
119.9 120.7 120.5
bromide exo-anti-Tricyclo[3.1.1.0234]heptan-6-yl p-bromobenzoate anti-8-Tricyclo[3.2.1 . 0 2 ~ 4 ] o ~p-bromobenzenesulfonate tyl 1 -Cyanosemibullvalene
L324 (L3'24)
f542 (L5'42)
Ref
119.0
116.0 (114.4)
120.5 120.4 116.8 115.5 120.5 118.8 118.8 (115.8) 115.9 (116.2) 103
119.5 118.7 116.5 116.2 118.9 118.1 121.9
fl
b C
d e
f g h i
122.0
i
112
k
107.6
(1 14) 108.8 (1 29.9)
k
107.5
106.4
1
100 104.9 104.8
m n This work
98 105.7 106.1
a R. Karlsson, Acta Crystallogr., Sect. B, 32, 2609-2614 (1976). R . A. Kershaw, Ph.D. Thesis, Ohio State University, 1974. G . R. Clark and G. J. Palenik, J . Chem. Soc., Perkin Trans. 2, 194-197 (1973). G. W.Henslee, J. D. Woodyard, and J. D. Oliver, Acta Crystallogr., Sect. E , 32,2880-2883 (1976). e G. Maas, K. Fischer, and M. Regitz, ibid., 30, 1140-1 145 (1974).f G .Maas, K. Fischer, and M. Regitz, ibid., 30,2853-2860 (1974).g J. D. Oliver, G. Henslee, and P. E. Rush, ibid., 32,2274-2278 (1976). C . J. Fritchie, Jr., Acta Crystallogr., 20,27-36 (1966). G. D. Anderson, R. S. McEwen, and W. Herz, Acta Crystallogr., Sect. B, 29,2783-2789 (1973).J L.J. Guggenberger and R. A. Jacobson, ibid., 25,888-894 (1969). R. C . Pettersen, 0.Kennard, and W. G. Dauben, J . Chem. SOC., Perkin Trans. 2, 1929-1935 (1972). F. R. Ahmed and E. J. Gabe, Acta Crystallogr., 17,603-608 (1964). S. Masamune, R. Vukov, M. J. Bennett, and J. T . Purdham, J . Am. Chem. SOC., 94,8239-8241 (1972). A. C . Macdonald and J. Trotter, Acta Crystallogr., 18, 243-249 (1965).
toward coplanarity of the individual a systems and a shortened C ( 1)-C(6) distance. Since these systems provide their own difficulties to proving whether the C(1)- C ( 6 ) contact is attractive or repulsive, the more appropriate comparison is afforded by the cyclophanes, which do not undergo such rearrangements. The very short contacts between the directly opposed a-orbital lobes in cyclophane compounds are invariably accompanied by very severe bond distance and bond angle distortions (e.g., C(2) is displaced 0.12 %, from the plane of C ( l)-C(6)-C(4)-C(3), and C(7)-C(8) is stretched to 1.568 (1) A).33One could argue that the a lobes in the semibullvalenes are not opposed head-on, as in the cyclophane systems, but are angled toward a point substantially below the line of centers C(4)- .C(6), as shown in Figure 6a, thus considerably reducing the magnitude of their interaction. A semiquantitative measure of the interpenetration of these p-a orbitals is provided by the size of the overlap integrals of the opposed p-orbital wave functions.34Implicit in such an overlap calculation are the assumptions that (1) the orientation of the orbitals can be accurately specified, (2) the orbitals contribute fully to the ground state molecular wave function, (3) they are fully populated, and (4) we have chosen the appropriate signs for the orbital wave functions. Assuming the validity of ( l ) , (2), and ( 3 ) 3 5and choosing opposite signs for the wave functions (antibonding configuration) oriented as in Figure 6, we find the value of the overlap integrals36 to be -0.09 for 1 cyanosemibullvalene and -0.10 for [2.2]metacyclophane. The
-
eo.
a1 150, 60 0'
bl 160. 6 4 5 '
CI I
dl 2 00, 83 6.
el
11 2 4 5 , 1095'
2 35, 103 I'
737'
Figure 6. Position and orientation of orbitals of atoms C(2) and C(8), projected onto the plane C( I)-C(Z)-C(X),as a function of the C(2)-C(8) interatomic separation. The C(2)-C(8) distance (A) and the C(2)C( l)-C(3) angle are given for (a) the formal structure Vlla, (b) geometry close to that observed for I-cyanosemibullvalene, (c) a point close to the symmetric transition state, (e) the geometry observed for the C(4)C(5)-C(6) end of I-cyanosemibullvalene, and (f) the formal structure Vllb.
magnitudes of these numbers are comparable; that we do not observe in 1-cyanosemibullvalene the severe bond length-bond angle distortions expected for a repulsive interaction of this size, but in fact the contrary, that (1) the dihedral angles are not unusual, (2) the C(4)-C(S)-C(6) angle is compressed rather than expanded, and (3) the cyclopentene rings have less pucker than normal, lead us to conclude that rather than a
3162
Journal of the American Chemical Society
Transition Stota
1OO:lO
/ May 10, 1978
the former at the extended Hiickel level and the latter a t the M I N D 0 / 2 and M I N D 0 / 3 levels of approximation. The Huckel calculations were based on assumed or only partially optimized geometries and the full details of the geometry optimization and wave functions of the M I N D 0 studies were not reported. We have consequently begun examining the 1-cyano- and semibullvalene rearrangement pathways using the minimum basis PRDDO method40 and the observed x-ray coordinates for the initial geometry. Full geometry optimization of the ground state satisfyingly reproduces the observed structure. Although this work is not complete, some qualitative statements can be made about the changes that occur in the course of the rearrangement and how these reflect on our understanding of the ground-state geometry. For the purpose of illustration we can conveniently, and reasonably accurately, consider all of the carbon atoms to be sp2 hybridized. Movement along the reaction pathway consists principally of concerted displacements of C(4) and C(6) toward each other and of C(2) and C(8) outward, causing the five-membered rings to become somewhat more planar as the transition state is approached and the C(3)-C(4) and C(6)-C(7) double bonds to delocalize into two strongly interacting allylic systems. The reorientations of the involved orbitals as the reaction progresses are more subtle but equally important: initially aligned in classical Walsh orbital fashion, toward the center of the cyclopropane ring, the sp2 lobes of C(2) and C(8) rotate about the C(2)-C(3) and C(8)-C(7) bonds so as to point toward C(1) (Figure 6 ) . The dissolution of the exocyclic cyclopropane Walsh orbital overlaps is compensated by the formation of conventional sp2-sp3 o bonds to a rehybridized C ( l ) , and by the incipient formation of the allylic systems. The orientations of C(4) and C(6), being coupled with C(2) and C(8), change simultaneously but in the opposite directions. It can be seen from purely symmetry arguments that the pz orbital involvements of C(3) and C(7) in the top two HOMOS (and consequently the extent of localization of the double bonds) are critically sensitive to the position along the reaction path, being zero at the transition state and opposite in sign at the antipodes of the rearrangement (Figure 7). Why then do we not find significant changes in the C(2)-C(3) and C(3)-C(4) bond distances in the 1-cyanosemibullvalene crystal structure? The answer is that the C(2)-C(8) and C(4). C ( 6 ) distances are simply much more sensitive functions of the bond order; the bond distance-bond order relationship is strongly nonlinear in the range 0 < B.O.
